Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

SECTION A] ON CARDINAL NUMBERS OF ASSIGNED TYPES

29

*102'32. I. Nc (%)'( = D"1(a Jq) AU(3}
Dent.
F.102*0325.)
F y e Nc (ao)'3.8 (HRl). R, E L -i lp. D'R = y. (1R = (.
4 -[*33-61] r (-,Al) II e 1" - IP. -Re f'6. 1)YR =,Y.
4 -[*33-123.*37-1] yE DCj~l - lP) (1%3}: ) F. Prop
*102-34. ~.N a )6=IL~,I~~Z()Reto 2I ' ' )
[Proof as in *102-31]
*102-35. F. Nc D,3) (1=D - 1 (,)} A'(] [Proof as in *102-32]
*102-36. F. E! Nc (ap)'( [*102-31. *1421]
This proposition is true whenever it is significant, and is significant
whenever 8e t'fl. When ( belongs to somie other type, the above proposition
is not significant.
*102-361. F.E!Nc(a,,3)'(3 [*102,34. *1421]
*102-37. F. U'Nc (ap) = t'/
Dern.
F. *37-402. (*65-1 1). D F. (PNe(ap) C t'I (1)
F.*10236.*3343. )F. (. (3eCl'Nc(a,3).
[*63141 ) F-. t0'U'CNc (ap) = II'Nc (ap) (2)
* (1). *63 21. F. t'cli'Nc (ap) = t'c3 (3)
F.(2).(3).) F. Prop
*102-4. F*: yENc(cB)'(.'eNC(cs)'(3. ). 7ENc (aa)"y' [*102-3-26]
*102-41. F: 7ENc (a*)'(. "7 eNc(a'p)'(3. ). YE Ne (c,)'y' [*102-3-27]
*102A42. F. a E Nc(a)'a [*1023-2. *73-3. *63-103]
*102-43. F. a! Nc (a,,)'a [*102-42]
This inference is legitimate because, when a is given, " Nc (a,)'a" is
typically definite. The inference from "a E Nc'a" (which is true) to "! HNc'a"
is not valid, because "! Nc'a" may hold only for some of the possible
determinations of the ambiguity of " Nc."
*102 44. F:asmnfl..aENc(arg)'fl..I3ENc(fl)'a
Dem.
F.*63 102.)
F( 2 a smF'8. =-.Paope t~a. p E t 8
F.(1). *102-2,3 -:) F Prop